Mean Absolute Deviation - Decimals Worksheet - Free Printable

Let’s solve each problem step by step. We’ll find the mean, then the difference from the mean for each number, take the absolute value of those differences, sum them up, and divide by how many numbers there are — that’s the Mean Absolute Deviation (MAD).

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Problem 1: Data = 21.3, 11.5, 51.6, 35, 18.8, 49

Step 1: Find the Mean

Add all numbers:
21.3 + 11.5 = 32.8
32.8 + 51.6 = 84.4
84.4 + 35 = 119.4
119.4 + 18.8 = 138.2
138.2 + 49 = 187.2

There are 6 numbers → Mean = 187.2 ÷ 6 = 31.2

Step 2: Find Differences from Mean

- 21.3 - 31.2 = -9.9
- 11.5 - 31.2 = -19.7
- 51.6 - 31.2 = 20.4
- 35 - 31.2 = 3.8
- 18.8 - 31.2 = -12.4
- 49 - 31.2 = 17.8

Step 3: Absolute Values

- | -9.9 | = 9.9
- | -19.7 | = 19.7
- | 20.4 | = 20.4
- | 3.8 | = 3.8
- | -12.4 | = 12.4
- | 17.8 | = 17.8

Step 4: Sum of Absolute Values

9.9 + 19.7 = 29.6
29.6 + 20.4 = 50.0
50.0 + 3.8 = 53.8
53.8 + 12.4 = 66.2
66.2 + 17.8 = 84.0

Step 5: MAD = Sum ÷ Number of Data Points

84.0 ÷ 6 = 14.00

✔ Final Answer for #1: 14.00

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Problem 2: Data = 63.4, 25.5, 25.9, 10.2

Step 1: Mean

63.4 + 25.5 = 88.9
88.9 + 25.9 = 114.8
114.8 + 10.2 = 125.0

4 numbers → Mean = 125.0 ÷ 4 = 31.25

Step 2: Differences

- 63.4 - 31.25 = 32.15
- 25.5 - 31.25 = -5.75
- 25.9 - 31.25 = -5.35
- 10.2 - 31.25 = -21.05

Step 3: Absolute Values

- |32.15| = 32.15
- |-5.75| = 5.75
- |-5.35| = 5.35
- |-21.05| = 21.05

Step 4: Sum

32.15 + 5.75 = 37.9
37.9 + 5.35 = 43.25
43.25 + 21.05 = 64.30

Step 5: MAD = 64.30 ÷ 4 = 16.075 → Round to two decimals: 16.08

✔ Final Answer for #2: 16.08

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Problem 3: Data = 63.5, 36.7, 27.2, 50.3, 21.5

Step 1: Mean

63.5 + 36.7 = 100.2
100.2 + 27.2 = 127.4
127.4 + 50.3 = 177.7
177.7 + 21.5 = 199.2

5 numbers → Mean = 199.2 ÷ 5 = 39.84

Step 2: Differences

- 63.5 - 39.84 = 23.66
- 36.7 - 39.84 = -3.14
- 27.2 - 39.84 = -12.64
- 50.3 - 39.84 = 10.46
- 21.5 - 39.84 = -18.34

Step 3: Absolute Values

- 23.66
- 3.14
- 12.64
- 10.46
- 18.34

Step 4: Sum

23.66 + 3.14 = 26.8
26.8 + 12.64 = 39.44
39.44 + 10.46 = 49.9
49.9 + 18.34 = 68.24

Step 5: MAD = 68.24 ÷ 5 = 13.648 → Round to two decimals: 13.65

✔ Final Answer for #3: 13.65

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Problem 4: Data = 31.6, 34.5, 29.8, 12.1

Step 1: Mean

31.6 + 34.5 = 66.1
66.1 + 29.8 = 95.9
95.9 + 12.1 = 108.0

4 numbers → Mean = 108.0 ÷ 4 = 27.0

Step 2: Differences

- 31.6 - 27.0 = 4.6
- 34.5 - 27.0 = 7.5
- 29.8 - 27.0 = 2.8
- 12.1 - 27.0 = -14.9

Step 3: Absolute Values

- 4.6
- 7.5
- 2.8
- 14.9

Step 4: Sum

4.6 + 7.5 = 12.1
12.1 + 2.8 = 14.9
14.9 + 14.9 = 29.8

Step 5: MAD = 29.8 ÷ 4 = 7.45

✔ Final Answer for #4: 7.45

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Problem 5: Sales Increase (%) — Cars: 7.8, Motorbikes: 6.2, Jeeps: 3.3, Trucks: 2.6, Tractors: 1.4

Step 1: Mean

7.8 + 6.2 = 14.0
14.0 + 3.3 = 17.3
17.3 + 2.6 = 19.9
19.9 + 1.4 = 21.3

5 items → Mean = 21.3 ÷ 5 = 4.26

Step 2: Differences

- 7.8 - 4.26 = 3.54
- 6.2 - 4.26 = 1.94
- 3.3 - 4.26 = -0.96
- 2.6 - 4.26 = -1.66
- 1.4 - 4.26 = -2.86

Step 3: Absolute Values

- 3.54
- 1.94
- 0.96
- 1.66
- 2.86

Step 4: Sum

3.54 + 1.94 = 5.48
5.48 + 0.96 = 6.44
6.44 + 1.66 = 8.10
8.10 + 2.86 = 10.96

Step 5: MAD = 10.96 ÷ 5 = 2.192 → Round to two decimals: 2.19

✔ Final Answer for #5:
Mean = 4.26
Mean Absolute Deviation = 2.19

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Final Answer:
1) 14.00
2) 16.08
3) 13.65
4) 7.45
5) Mean = 4.26, Mean Absolute Deviation = 2.19